Nicholas J. Giordano
www.cengage.com/physics/giordano
Introduction
The Purpose of Physics
• What does the word physics mean?
• A connection with natural philosophy
• Organized around a collection of natural laws
• Wants to predict how the world works
• Wants to understand why the world works the way it does
Section 1.1
What is Physics?
• The science of matter and energy, and the interactions
between them
• Matter and energy are fundamental to all areas of science
• Physics is a foundational subject
• Principles of physics form the basis of understanding other
sciences
• Allows us to understand things from very large to very small
Section 1.1
What is Physics?, cont.
• The study of the natural or material world and phenomena
• Meaning of physics from the Greek for nature
• Natural philosophy
• Oldest science
• All scientists were originally physicists
Section 1.1
Studying Physics
• Goal is to predict and understand how the universe works
• Organized around physical laws
• What do the laws say?
• How can we apply the laws to new situations?
• Mathematics
• The laws are generally expressed mathematically
Section 1.1
Isaac Newton
• Mechanics will be the first
area studied
• Laws were developed by
Sir Isaac Newton
• 1642 - 1727
• Laws of Motion
• Apply to a wide variety of
objects
Section 1.1
Overall Goals
• Predicting how the world works
• Use the physical laws for predictions
• Understanding why it works the way it does
• Where do the physical laws come from?
• May be helpful to examine the form of the physical law
Section 1.1
Problem Solving
• Problem solving is the process of applying a general
physical law to a particular case
• An essential part of physics
• Processes apply to many different situations
• Takes practice
Section 1.2
Types of Problems
• We will encounter various types of problems
• Quantitative problems
•
Give numerical information and use calculations
• Concept checks
•
Test your general understanding of a law and its application
• Reasoning and relationship problems
•
Identify what important information might be “missing”
• Successfully dealing with these types of problems is
essential to gaining a thorough understanding of physics
Section 1.2
Problem Solving Strategies
• Recognize the key physics principles
• Need a conceptual understanding of the laws, how they are
applied, and how they are interrelated
• Sketch the problem
• Show the given information
• Generally includes a coordinate system
Section 1.2
Problem Solving Strategies, cont.
• Identify the important relationships
• Use the given information and the unknown quantities to
determine what laws apply
• May involve substeps
• Solve for the unknown quantities
• Check
• What does it mean?
• Does the answer make sense?
• Think about your answer
Section 1.2
Dealing With Numbers
• There are numerous techniques you will encounter when
dealing with numbers including
• Scientific notation
• Significant figures
•
•
Recognizing them
Using them in calculations
Section 1.3
Scientific Notation
 Scientific notation is a useful way to write numbers that
are very large or very small
 To write a number in scientific notation:
 Move the decimal point to create a new number between 1
and 10

Not including 10
 Count the number of places the decimal point was moved



This is the exponent of 10
The exponent is positive if the original number is greater than one
The exponent is negative if the original number is less than one
Section 1.3
Significant Figures
• There is an uncertainty associated with all measurements
• Uncertainty is also called experimental error
• Values are written using significant figures
• A digit is significant if it is meaningful with regard to the
accuracy of the value
• Zeros may be ambiguous
• Scientific notation helps clarify the significance of any zeros
Section 1.3
Significant Figures, Examples
 Example: 100
 May have 1 significant figure

Zeros are ambiguous
 Rewrite in scientific notation

1.00 x 102 shows 3 significant figures
 Example: 0.00123
 3 significant figures
 In numbers less than 1, zeros immediately to the right of the
decimal point are not significant
 Can also be clarified by writing in scientific notation: 1.23
x 10-3
Section 1.3
Significant Figures in Calculations
• Multiplication and division
• Use the full accuracy of all known quantities when doing
the computation
• At the end of the calculation, round the answer to the
number of significant figures present in the least accurate
starting quantity
• Example: 976 x 0.000064 m = 0.062464 m~ 0.062 m
•
Due to the 2 significant figures in the 0.000064 m
Section 1.3
Rounding Error
• In multiple step problems, you could round at different
steps
• Different final values may be obtained
• These differences are the rounding error
• Carry an extra significant figure through intermediate
steps in the computation and perform the final rounding at
the very end
Section 1.3
Significant Figures in
Calculations, cont.
• Addition and subtraction
• The location of the least significant digit in the answer is
determined by the location of the least significant digit in
the starting quantity that is known with the least accuracy
• Example: 4.52 + 1.2 = 5.72 ~ 5.7
•
Due to the location of the significant digit in the 1.2
Section 1.3
Exact Numbers
• Some values are exact
• Not measured
• Defined
• Examples
•
1 min = 60 sec
• Appears to have 1 significant figure, but it is a definition
• Can be thought of as 60.00000000… seconds
• The number of significant figures in a calculation is
determined by the number of significant figures in other
quantities involved
Section 1.3
Physical Quantities and
Units of Measure
• When conducting experiments, you must be able to
measure various physical quantities
• Will often deal with units of
• Length
• Time
• Mass
• Will use SI system
• Include prefixes and powers of 10
Section 1.4
Units of Measure
• Each measured quantity must have a unit of measure for
that quantity
• Three basic quantities
• Length (or distance)
• Mass
• Time
Section 1.4
Definition of the Meter
• The original definition of a
meter was in terms of the
Earth’s circumference
• Then changed to be based
on this platinum-iridium
bar
• Now defined in terms of
the wavelength of light
emitted by krypton atoms
• See table 1.1 for some
common length values
Section 1.4
Converting Between Units
• Use a conversion factor
• Relates the two units of interest
• Express in fractional form
•
The fraction will be equal to 1 and so not change the actual value,
just how it is expressed
• Multiply the original quantity by the conversion factor to
obtain the new expression of the quantity
Section 1.4
Definition of a Second
• The value of the second is
based on the frequency of
light emitted by cesium
atoms
• Shown is a cesium clock
in the National Institute of
Standards and Technology
• See table 1.2 for some
example times
Section 1.4
Definition of Kilogram
• Mass is related to the
amount of material
contained in the object
• Defined in terms of a
standard kilogram
• Composed of platinum
and iridium
• See table 1.3 for some
common mass values
Section 1.4
Standard Units
• Units of measure must be standardized
• Makes the units useful
• Makes communication about the units possible
• Système International d’Unitès
• Commonly called the SI system
• Primary units of length, mass and time are the meter,
kilogram and second
Section 1.4
Other Systems
• CGS
• Uses centimeters (length), grams (mass) and seconds (time)
• U.S. Customary System
• Uses feet (length), slugs (mass), and seconds (time)
Section 1.4
Units Summary
Section 1.4
Prefixes
• Prefixes can also be used to express very large or very
small numbers
• Prefixes represent various powers of 10
• Can be used with any unit
• See table 1.5 for various prefixes and their corresponding
power of 10
Section 1.4
Dimensions and Units
• Units of other quantities may be derived from the units
discussed so far
• There are seven primary units in the SI system
• All other units can be derived from these primary units
• Dimensional analysis
• Can be used to check problems
Section 1.5
Derived Units
• The primary units can be combined into derived units
• Some will be given special names
• Examples:
• m3
• kg/m3
• In mechanics, three primary quantities are needed to build
all the other necessary quantities
• Length, time, and mass
Section 1.5
Dimensions
• Dimensional analysis can be used to check problems
• Dimensions are
• Length – L
• Time – T
• Mass – M
• Dimensions are independent of the particular units
Section 1.5
Using Dimensional Analysis
• The dimensions must be the same on both sides of the
equals sign in an equation
• The dimensions will correspond to the units
• The dimensions are independent of the particular units used
to measure quanitites
• Using dimensions as a check can sometimes reveal errors
in a calculation
Section 1.5
Algebra and Simultaneous Equations
• Mathematical methods you may need to use include
• Algebra
• Trigonometry
• Vectors
• Chapter 1 reviews these
• Also information in Appendix B
Section 1.6
Checking Units
• The same approach used with dimensions can be used
with units
• The units need to be in the same system
• The units should be correct for the quantity being
calculated
• Always check the dimensions and units of your answer
Section 1.6
Trigonometry
• Generally will use only right
triangles
• Pythagorean Theorem
• r2 = x 2 + y 2
• Trig functions
• sin θ = y / r
• cos θ = x / r
• tan θ = y / x
• Trigonometric identities
• sin² θ + cos² θ = 1
• Other identities are given in
appendix B and the back
cover
Section 1.7
Inverse Functions and Angles
• To find an angle, you need
to use the inverse of a trig
function
• If sin θ = y/r then
θ = sin-1 (y/r)
• Angles in the triangle add
up to 90°
• α + β = 90°
• Complementary angles
• sin α = cos β
Section 1.7
Angle Measurements
• Various units
• Degrees
• Radians
• 360° = 2 π rad
• Definition of radian
• θ = s/ r
•
•
•
s is the length of arc
r is the radius
s and r must be measured in
the same units
Section 1.7
Vectors vs. Scalars
• A scalar is a quantity that requires only a magnitude (with
unit)
• A vector is a quantity that requires a magnitude and a
direction
Section 1.8
Vectors
• Vector quantities need special techniques
• Vectors may be
• Added
• Multiplied by a scalar
• Subtracted
• Resolved into components
Section 1.8
Vector Representation
 The length of the arrow
indicates the magnitude of
the vector
 The direction of the arrow
indicates the direction of the
vector with respect to a
given coordinate system
 Vectors are written with an
arrow over a boldface letter
 Mathematical operations can
be performed with vectors
Section 1.8
Adding Vectors
• Draw the first vector
• Draw the second vector
starting at the tip of the first
vector
• Continue to draw vectors
“tip-to-tail”
• The sum is drawn from the
tail of the first vector to the
tip of the last vector
• Example:
Section 1.8
Multiplying Vectors by Scalars
• Multiplying a vector by a
positive scalar only affects
the vector’s magnitude
• It will have no effect on
the vector’s direction
• Example:
• If
= 10.0 km @
10.0°and K = 2, then
= 20.0 km @ 10.0°
Section 1.8
Multiplying Vectors
by Scalars, cont.
• If K > 1, then the resultant vector is longer than the
original vector
• If K < 1 and positive, then the resultant vector is shorter
than the original vector
• If K is negative, then the resultant vector is in the opposite
direction from the original vector
• If
= 10.0 km @ 10.0° and K = - 2 then
= 20.0 km @ 190.0°
Section 1.8
Subtracting Vectors
 To subtract a vector, you add its opposite
Section 1.8
Components of Vectors
• The x- and y-components
of a vector are its
projections along the xand y-axes
• Calculation of the x- and
y-components involves
trigonometry
• Ax = A cos θ
• Ay = A sin θ
Section 1.8
Vector from Components
• If you know the
components, you can find
the vector
• Use the Pythagorean
Theorem for the
magnitude:
• Use the tan-1 to find the
direction:
Section 1.8
Adding Vectors Using Components
• Assume you are adding
two vectors:
• To add the vectors, add
their components
• Cx = Ax + Bx
• Cy = Ay + By
• Then the magnitude and
direction of C can be
determined
Section 1.8
Other Operations with Vectors
• To subtract vectors, again add the opposite vector using
the component method
• Multiplication of a vector by a scalar is done by
multiplying each component by the scalar
• These component techniques can also be applied in three
dimensions
Section 1.8